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xxMikexx [17]
3 years ago
5

Use the table and diagram to answer this question. (I attached the picture)

Mathematics
1 answer:
iragen [17]3 years ago
3 0
We have a right triangle with two of the legs known (7 and 4). The hypotenuse is unknown. Because of this, we will use the tangent trigonometric function.

Tangent of an angle is equal to the ratio of the opposite and adjacent sides
tan(angle) = opposite/adjacent

Divide those two sides to get
opposite/adjacent = 7/4 = 1.75

Look through the table and see which value in the "tan(x)" column is closest to 1.75, and that happens to be 1.7321. It is in the bottom row corresponding to 60 degrees.

So the final answer is choice D) 60 degrees

Note: it turns out that the angle theta is roughly 60.2551187 degrees

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(X^4)-(45x^2)+324 what are the zeroes? And how many turning points?
dmitriy555 [2]

Zeroes:

We must solve

x^4-45x^2+324=0

To do so, we define the auxiliary variable t=x^2. The equation becomes

t^2-45t+324=0

The quadratic formula yields the solutions

t=9,\quad t=36

Substituting back t=x^2 gives

x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6

So, the zeroes are -6, -3, 3, 6.

Turning points:

Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.

We have

f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x

If we set the derivative to be zero, we have

4x^3-90x=0 \iff x(4x^2-90)=0

So, the derivative is zero if x=0 or

4x^2=90 \iff 2x^2=45 \iff x^2=\dfrac{45}{2}\iff x=\pm\sqrt{\dfrac{45}{2}}

6 0
3 years ago
Mr Diaz decreased the speed of his car by 30 miles per hour over a period of 10 seconds. What is the average change in the speed
Allisa [31]
Divide 30 by 10. 30mph/10seconds = 3mph/seconds
4 0
3 years ago
.Nisha bought a backpack that was on sale at 35% off for $63. How much was the original price of the backpack?
Vlad [161]

Answer:

$180

Step-by-step explanation:

100%=x

35%=$63

63 x 100=6300/35=$180

3 0
3 years ago
Read 2 more answers
The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and length
cestrela7 [59]

Answer:

Width: 15 Length: 53

Step-by-step explanation:

7 0
3 years ago
The ratio of boys to girls in a group is 7:3. If there are 40 more boys than girls, work out how many people there are in total.
LenaWriter [7]

Answer:

Step-by-step explanation:

7 - 3 = 4

7 + 3 = 10

4/10 = 40

10/10 = ?

10/10 x 40 x 10/4

= 100 people

7 0
3 years ago
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