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3 years ago

Help me find surface area of this shape

Mathematics

1 answer:

lozanna [386]3 years ago

4 0

The triangle <span>pyramid</span> is made up of 4 triangles.

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Formula:
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Area of triangle = 1/2 x base x height

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Area of the bottom triangle:
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Area = 1/2 x 9 x 7.8
Area = 35.1 yd²

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Area of the 3 side triangles:
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Area = 3 [ 1/2 x 9 x 10 ]
Area = 135 yd²

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Total Area:
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Total Area = 135 + 35.1
Total Area = 170.1 yd²

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Answer: Surface Area = 170.1 yd².
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A basketball with a diameter of 9.5 in. is placed in a cubic box with sides 15 in. long. How many cubic inches of packing foam a

Doss [256]

Answer:

The volume of foam needed to fill the box is approximately 2926.1 cubic inches.

Step-by-step explanation:

To calculate the amount of foaming that is needed to fill the rest of the box we first need to calculate the volume of the box and the volume of the ball. Since the box is cubic it's volume is given by the formula below, while the formula for the basketball, a sphere, is also shown.

Vcube = a³

Vsphere = (4*pi*r³)/3

Where a is the side of the box and r is the radius of the box. The radius is half of the diameter. Applying the data from the problem to the expressions, we have:

Vcube = 15³ = 3375 cubic inches

Vsphere = (4*pi*(9.5/2)³)/3 = 448.921

The volume of foam there is needed to complete the box is the subtraction between the two volumes above:

Vfoam = Vcube - Vsphere = 3375 - 448.921 = 2926.079 cubic inches

The volume of foam needed to fill the box is approximately 2926.1 cubic inches.

4 0

3 years ago

Find the solutions to x⁴-5x²-36=0 and the x-intercepts of the graph of y=x⁴-5x²-36.

disa [49]

Answer:

The solutions $x^4-5x^2-36=0$ are $x=3,\:x=-3,\:x=2i,\:x=-2i$ and the x-intercepts of $y=x^4-5x^2-36$ are $x=3,\:x=-3$

Step-by-step explanation:

Finding the solutions to $x^4-5x^2-36$ means finding the roots, a root is where the function is equal to zero.

The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.

To find the roots you need to:

Rewrite the equation with $u=x^2$ and $u^2=x^4$

$u^2-5u-36=0$

Solve by factoring

$\mathrm{Break\:the\:expression\:into\:groups}\\u^2-5u-36=\left(u^2+4u\right)+\left(-9u-36\right)$

$\mathrm{Factor\:out\:}u\mathrm{\:from\:}u^2+4u=u\left(u+4\right)$

$\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9u-36=-9\left(u+4\right)$

$u^2-5u-36=u\left(u+4\right)-9\left(u+4\right)$

$\mathrm{Factor\:out\:common\:term\:}u+4\\\left(u+4\right)\left(u-9\right)$

$u^2-5u-36=\left(u+4\right)\left(u-9\right)=0$

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions to the quadratic equation are:

$\:u=-4,\:u=9$

Substitute back $u=x^2$ , solve for x

$x^4-5x^2-36=(u-9)(u+4)=(x^2-9)(x^2+4)$

Apply the difference of squares formula

$x^4-5x^2-36=(x^2-9)(x^2+4)=(x-3)(x+3)(x^2+4)$

$(x-3)(x+3)(x^2+4)=0$

Using the Zero factor Theorem: if ab = 0 then a = 0 or b = 0 (or both a = 0 and b = 0)

The solutions are:

$\:x=3,\:x=-3,\:x=2i,\:x=-2i$

Because two of the solutions are complex roots the only x-intercepts are $x=3,\:x=-3$

3 0

3 years ago

At the zoo there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there

Alex777 [14]

lions = x

monkeys = 3x ( 3 times as many )

3x +x = 24

4x = 24

x = 24/4

x = 6

6 lions

6*3 = 18 monkeys

3 0

3 years ago

What is the volume of the sphere shown below??<br> R=13

kvasek [131]

Here is your answer

D. $\frac{8788}{3}$ π ${units}^{3}$

REASON:

Formula for volume of sphere

= 4/3×π× r^3

Here, r= 13

So,

volume=4/3×π× 13^3

= 4/3×π× 2197

= 8788/3 ×π

HOPE IT IS USEFUL

3 0

3 years ago

Figure B is a scaled copy of Figure A.

zimovet [89]

Answer:

Step-by-step explanation:

We are told that figure B is a scaled copy of B, which means figure A was enlarged by a certain scale factor to get a similar figure as A, now referred to as figure B.

The scale factor = ratio of any two corresponding sides of both similar figures.

Thus,

Scale factor of the similar figures given = 40/10 = 4.

This means that, figure A was scaled up by 4 times its original size to get figure B. Each side of figure B is 4 × the corresponding side in figure A.

Scale factor = 4

7 0

3 years ago