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3 years ago

Find the area for a triangle that has a base of 24 inches and a height of 4 inches

Mathematics

2 answers:

Bond [772]3 years ago

5 0

Answer:

Step-by-step explanation:

svlad2 [7]3 years ago

3 0

Answer:

48 in^2.

Step-by-step explanation:

Area of the triangle = 1/2 * base * height

= 1/2 * 24 * 4

= 1/2 * 96

= 48 in^2.

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Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

2 years ago

I don’t understand this question. Can anyone help? I need answers ASAP. Thanks for all the help

zavuch27 [327]

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

7 0

3 years ago

WILL GIVE BRAINLEIST!!!

sesenic [268]

Considering that the data has no outliers, the mean of 3.2 inches should be used to describe the center of the data represented in this line plot.

<h3>What measure should be used to describe the center of a data-set?</h3>

It depends if the data-set has outliers or not.

If it does not have outliers, the mean should be used.

If it has, the median should be used.

The dot plot gives the number of times each measure appears. Since there is no outliers, that is, all values are close, the mean should be used. It is given by:

M = (2 x 1 + 3 x 2 + 2 x 3 + 1 x 5 + 1 x 6 + 1 x 7)/(2 + 3 + 2 + 1 + 1 + 1) = 3.2 inches.

The mean of 3.2 inches should be used to describe the center of the data represented in this line plot.

More can be learned about the mean of a data-set at brainly.com/question/24628525

5 0

2 years ago

Read 2 more answers

Please find the missing number and please don’t refer me to a link thank youu

svlad2 [7]

Answer:

i don't know the answer BUT you can go to khan academy or tutor.com. Both can help :) good luck btw

Step-by-step explanation:

7 0

3 years ago

In the figure below, the two triangular faces of the prism are fight triangles with sides of length 3, 4, and 5. The other three

olasank [31]

The figure of the prism is attached below.

The total surface area of the prism equals the sum of areas of two triangles and the three rectangles.

Surface Area of Prism = Area of 2 Triangles + Area of 3 Rectangles.

Area of a Triangle = 0.5 x Base x Height
Area of a Triangle = 0.5 x 3 x 4 = 6 square units

There are 3 rectangles. From the figure we can see that the bottom most rectangle has the dimensions 4 by 6. The left most rectangle has the dimensions 3 x 6 and the right most rectangle has the dimensions 5 by 6.

So, the Area of 3 rectangles will be = (4 x 6) + (3 x 6) + (5 x 6) = 72 square units

The Surface Area of the prism will be:

Surface Area = 2 (4) + 72 = 84 square units

Thus the correct answer is option A

6 0

3 years ago