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3 years ago

At what point on the curve y=x^4 does the normal line have slope 16?

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

8 0

the answer would be (1, 7). because slope=change in y/change in x

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An isosceles triangle ABC with the base BC is inscribed into a circle. Find the measure of angles of it, if measure of arc BC=10

zzz [600]

Answer:

The measures of the angles of ΔABC are

m∠A = 51° , m∠B = 64.5 , m∠C = 64.5°

Step-by-step explanation:

* Lets revise some facts in the circle

- The measure of the circle is 360°

- Equal chords intercept equal arcs

- The measure of an inscribed angle equals half the measure

of the intercepted arc

* Lets solve the problem

- ΔABC is isosceles withe base BC

∴ AB = AC

- The vertex angle is A

∵ ∠A is an inscribed angle subtended by arc BC

∴ m∠A = 1/2 the measure of arc BC

∵ The measure of arc BC = 102° ⇒ given

∴ m∠A = 1/2(102) = 51°

- In ΔABC

∵ AB = AC ⇒ proved

∴ m∠B = m∠C ⇒ base angles of isosceles Δ

- The sum of the interior angles in any Δ = 180°

∵ m∠A = 51 ⇒ proved

∴ m∠B = m∠C = (180 - 51) ÷ 2 = 129 ÷ 2 = 64.5°

* The measures of the angles of ΔABC are

m∠A = 51° , m∠B = 64.5° , m∠C = 64.5°

5 0

2 years ago

Read 2 more answers

Tom rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 21.

Ber [7]

The probability of getting a total that is a factor of 21 is 0.22

<u>Explanation:</u>

Factor of 21 is = 1, 3, 7, 21

Out of all the factors of 21, we cannot get 21 when the two die are rolled as the maximum sum that can be obtained is 12

The possible combinations are:

(1,2) (1,6)

(2,1) (2,5)

(3,4)

(4,3)

(5,2)

(6,1)

Total outcome = 6 X 6

= 36

Number of outcomes that is the factor of 21 is 8

The probability of getting a total that is a factor of 21 is $\frac{8}{36}$

p(21) = 0.22

Therefore, the probability of getting a total that is a factor of 21 is 0.22

5 0

3 years ago

The first 5 terms of a quadratic sequence are

Mashcka [7]

Step-by-step explanation:

an = 2n^2 - 3 · Anonymous. -1, 5, 15, 29, 47, ... an = 2 n^2 - 3.

8 0

2 years ago

In the figure CD is the perpendicular bisector of AB . If the length of AC is 2x and the length of BC is 3x - 5 . The value of x

Dennis_Churaev [7]

Answer

Find out the value of x .

To proof

SAS congurence property

In this property two sides and one angle of the two triangles are equal.

in the Δ ADC and ΔBDC

(1) CD = CD (common side of both the triangle)

(2) ∠CDA = ∠ CDB = 90 °

( ∠CDA +∠ CDB = 180 ° (Linear pair)

as given in the diagram

∠CDA = 90°

∠ CDB = 180 ° - 90°

∠ CDB = 90°)

(3) AD = DB (as shown in the diagram)

Δ ADC ≅ ΔBDC

by using the SAS congurence property .

AC = BC

(Corresponding sides of the congurent triangle)

As given

the length of AC is 2x and the length of BC is 3x - 5 .

2x = 3x - 5

3x -2x =5

x = 5

The value of x is 5 .

Hence proved

7 0

2 years ago

Read 2 more answers

Harold has four classes each school morning each class is an hour long and there is 10 minutes between classes the first class s

Y_Kistochka [10]

The 4th class ends at 12:40

3 0

2 years ago