A square pyramid has a base length of 7 meters and a slant height of 11 meters. what is the surface area

A telephone pole has a wire attached to its top that is anchored to the ground. the distance from the bottom of the pole to the

kirza4 [7]

The height of the pole is 96 feet

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]

$a^{2}+b^{2}=c^{2},$

Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.

Set up the equation $h^2 + (h - 68)^2 = (h + 4)^2$ using the Pythagorean theorem ( $a^2 + b^2 = c^2$ ).

$h^2 + (h - 68)^2 = (h + 4)^2$

On simplifying we get

$h^2+h^2-136h+4624 = h^2+8h+16$

$2h^2-136h+4624=h^2+8h+16$

$h^2-144h+4608=0$

Solving using quadratic formula

$h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}$

$h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}$

h1 = 96 feet , h2 = 48 feet

If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .

Hence the height of the pole is 96 feet

Learn more about Pythagoras theorem here :

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7 0

2 years ago

Can someone help will all the problems I will mark you the brainest!

lyudmila [28]

Answer:

1. C = 29.52 inches A = 69.63 square inches

2. C = 28.26 inches A = 63.59 square inches

3. Each side of the lawn is 13 yards.

4. 7 is a rational number ( $\frac{14}{2}$ ), a whole number, and an integer.

5. x = 16

6. h = 12.4

Step-by-step explanation:

1.

π = 3.14

The formula for the circumference of a circle that uses radius is C = 2πr.

C = 2 × 3.14 × 4.7 --- plug in known info

C = 29.516 inches --- solve

C = 29.52 inches

The formula for the area of a circle that uses radius is A = πr².

A = 3.14 × 4.7² --- plug in known info

A = 3.14 × 22.09 --- solve

A = 69.3626 square inches --- solve

A = 69.63 square inches

2.

The formula for the circumference of a circle that uses diameter is C = πd.

C = 3.14 × 9 --- plug in known info

C = 28.26 inches --- solve

To solve for area with the diameter, divide it by 2 and use the radius area formula.

$\frac{9}{2}$

r = 4.5

A = πr²

A = 3.14 × 4.5² --- plug in known info

A = 3.14 × 20.25 --- solve

A = 63.585 square inches --- solve

A = 63.59 square inches

3.

Because the lawn is square, the length and width of the lawn are equal.

Let x = the length and width.

x × x = 169 --- l × w = area of rectangle

x² = 169 --- x × x is the same as x²

x = 13 --- square root both sides to get rid of square on x

Each side of the lawn is 13 yards.

4.

√49 = 7

Rational number: a number that can be expressed as a simple fraction of 2 integers, 7 = $\frac{14}{2}$

Irrational number: a number that cannot be expressed as a simple fraction of 2 integers, √2

Whole number: All natural numbers, including 0, up to infinity, 0, 1, 2, 3, 4, 5...

Integer: All whole numbers and their negative counterparts -4, -3, -2, -1, 0, 1, 2, 3, 4…

7 is a rational number ( $\frac{14}{2}$ ), a whole number, and an integer.

5.

We can solve for x using the Pythagorean theorem: If a triangle is right, a² + b² = c².

12² + x² = 20² --- plug in known info

144 + x² = 400 --- solve

x² = 256 --- subtract 144 from both sides

x = 16 --- square root both sides

6.

Same as problem 5, we will use the Pythagorean theorem to solve.

3² + 12² = h² --- plug in known info

9 + 144 = h² --- solve

153 = h² --- solve

h = 12.36931688 --- square root both sides

h = 12.4 --- round to nearest 10th

6 0

3 years ago

Evaluate the expression w² - v + 1 for w = -2 and v = -8.

kaheart [24]

Answer:

13

Step-by-step explanation:

-2(-2) - (-8) + 1

4 + 8 + 1 = 13

7 0

3 years ago

Read 2 more answers

How would I find x when there is a arrow pointing down instead of up<br><br> What does x equal to??

lys-0071 [83]

Since opposite exterior angles are congruent I would plug in numbers for X till you find a number that goes into both and gets you the same product.

7 0

3 years ago

Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$

This is the slope of the tangent line, which has equation

$y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}$

7 0

3 years ago